Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
All Direct removal and addition 448 Alligation cross rule 270 Ratios, quantities, and percentages 233 Weighted mean and concentration 195 Equal quantity replacement 189 Three or more components 174 Repeated equal-volume replacement 154 Profit-based alligation 153

Mixtures and Alligation Questions

Multiple choice

A milkman has a vessel containing 40 litres of milk. He delivers 10 litres to the first house, and adds an equal quantity of water to the vessel. He does exactly the same at the second and third houses. What is the ratio of milk and water when he has finished delivering at the third house and added 10 litres of water?

  1. 27 : 37

  2. 26 : 38

  3. 1 : 4

  4. 27 : 64
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The amount of milk remaining after 3 operations is 40 * (1 - 10/40)^3 = 40 * (3/4)^3 = 40 * 27/64 = 16.875. The water is 40 - 16.875 = 23.125. The ratio 16.875 : 23.125 simplifies to 27 : 37.

Multiple choice

The ratio of metal 1 and metal 2 in alloy A is 3 : 4. In alloy B, the same metals are mixed in the ratio 5 : 8. If 26 kg of alloy B and 14 kg of alloy A are mixed, then find out the ratio of metal 1 and metal 2 in the new alloy.

  1. 3 : 2

  2. 2 : 5

  3. 2 : 3

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Alloy A: 14 kg, ratio 3:4 (Total parts 7). Metal 1 = 14 * 3/7 = 6, Metal 2 = 8. Alloy B: 26 kg, ratio 5:8 (Total parts 13). Metal 1 = 26 * 5/13 = 10, Metal 2 = 16. Total Metal 1 = 6+10=16, Total Metal 2 = 8+16=24. Ratio = 16:24 = 2:3.

Multiple choice

120 L of a solution contains milk and water in the ratio 2 : 3. The volume of the solution is increased by 25% by adding water to it. From the resultant mixture, 30 L are drawn out and replaced by 30 L of milk. Find the ratio of milk to water in the final solution?

  1. 57 : 125

  2. 68 : 125

  3. 57 : 68

  4. 68 : 90
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial: 120L, 2:3 ratio -> 48L milk, 72L water. Increase volume by 25% (30L) by adding water: 48L milk, 102L water. Total 150L. Draw 30L: Ratio is still 48:102 (or 8:17). 30L contains (8/25)*30 = 9.6L milk and 20.4L water. Remaining: 38.4L milk, 81.6L water. Add 30L milk: 68.4L milk, 81.6L water. Ratio 68.4/81.6 = 684/816 = 57/68.

Multiple choice

A 5 litre jug contains 4 litres of salt water solution that contains 15 percent salt. If 1.5 litres of the solution spills out of the jug and the jug is filled to capacity with water, approximately what percent of the resulting solution in the jug is salt?

  1. 7.5%

  2. 9.5%

  3. 10.5%

  4. 12%

  5. 13%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial salt = 4 * 0.15 = 0.6 litres. After 1.5 litres spills, remaining solution = 2.5 litres. Remaining salt = 2.5 * 0.15 = 0.375 litres. Jug filled to 5 litres with water. New concentration = 0.375 / 5 = 0.075 = 7.5%.

Multiple choice

If 50g of water at a temperature of 30°C is added to 200g of water at a temperature of 100°C, what will the new temperature of the water be?

  1. 68°C

  2. 80°C

  3. 74°C

  4. 86°C

  5. 92°C
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The final temperature is calculated using the principle of heat exchange: m1*c*(T-T1) = m2*c*(T2-T). With 50g at 30C and 200g at 100C, the equation is 50(T-30) = 200(100-T), which simplifies to T-30 = 400-4T, or 5T = 430, resulting in T = 86C.

Multiple choice

A shopkeeper mixed two qualities of rice in the ratio 4 : 1 and sold the mixture at Rs. 72 per kg for a profit of 12.5%. If the cost of second quality of rice is Rs. 3.25 more per kg than the first quality of rice, what is the cost per kg of the rice of first quality?

  1. Rs. 63.75

  2. Rs. 63.35

  3. Rs. 62.83

  4. Rs. 62.45

  5. Rs. 62.23
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the cost of first quality be x and second be x + 3.25. Ratio 4:1. Total cost = (4x + 1(x + 3.25)) / 5 = (5x + 3.25) / 5 = x + 0.65. Selling price = 72, profit 12.5%. Cost = 72 / 1.125 = 64. So x + 0.65 = 64, x = 63.35.

Multiple choice

In solution of sugar and water the ratio of sugar and water by weight is 1:4. This solution is heated and in the process it loses 50% weight. What is the ratio of weight of sugar and water in the final mixture?

  1. 4:1

  2. 2:1

  3. 2:3

  4. 3:5

  5. 5:2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial ratio 1:4 means 1 unit sugar, 4 units water (total 5). If it loses 50% weight, 2.5 units remain. Since sugar is non-volatile, 1 unit of sugar remains, and 1.5 units of water remain. The new ratio is 1:1.5, which is 2:3.